Solve for $x$ and $y$ using substitution. ${5x+3y = 11}$ ${y = -3x+9}$
Solution: Since $y$ has already been solved for, substitute $-3x+9$ for $y$ in the first equation. ${5x + 3}{(-3x+9)}{= 11}$ Simplify and solve for $x$ $5x-9x + 27 = 11$ $-4x+27 = 11$ $-4x+27{-27} = 11{-27}$ $-4x = -16$ $\dfrac{-4x}{{-4}} = \dfrac{-16}{{-4}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {y = -3x+9}\thinspace$ to find $y$ ${y = -3}{(4)}{ + 9}$ $y = -12 + 9$ $y = -3$ You can also plug ${x = 4}$ into $\thinspace {5x+3y = 11}\thinspace$ and get the same answer for $y$ : ${5}{(4)}{ + 3y = 11}$ ${y = -3}$